Showing papers on "Wave height published in 1985"

A Fifth‐Order Stokes Theory for Steady Waves

Abstract: An alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself. The first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary. In addition to the usually specified design parameters of wave height, period and water depth, it is also necessary to specify the current or mass flux to apply any steady wave theory. The reason being that the waves almost always travel on some finite current and the apparent wave period is actually a Dopplershifted period. Most previous theories have ignored this, and their application has been indefinite, if not wrong, at first order. A numerical method for testing theoretical results is proposed, which shows that two existing theories are wrong at fifth order, while the present theory and that of Chappelear are correct. Comparisons with experiments and accurate numerical results show that the present theory ...

Wave height variation across beaches of arbitrary profile

Abstract: An intuitive expression for the spatial change in energy flux associated with waves breaking in the surf zone is developed. Using shallow water linear wave theory, analytical solutions for wave height transformation due to shoaling and breaking on a flat shelf, a plane slope, and an “equilibrium” beach profile are derived and then compared to laboratory data with favorable results. The effect of beach slope on wave decay is included explicitly, while wave steepness effects are included implicitly by specification of the incipient conditions. Set-down/set-up in the mean water level, bottom friction losses, and bottom profiles of arbitrary shape are introduced, and solutions are obtained numerically. The model is calibrated and verified using laboratory data with very good results for the wave decay but not so favorable results for set-up. A test run on a prototype scale profile containing two bar and trough systems demonstrates the model's ability to describe the shoaling, breaking, and wave re-forming process commonly observed in nature. Bottom friction is found to play a negligible role in wave decay in the surf zone when compared to shoaling and breaking.

Field Data on Seaward Limit of Profile Change

Abstract: Many coastal engineering problems require an estimate of the seaward limit of sediment transport, defined as the minimum depth at which no measurable change in water depth occurs. A procedure to estimate this limit depth was evaluated using measurements collected at the Coastal Engineering Research Center's Field Research Facility located on the Atlantic Ocean. The data consisted of measured wave characteristics and accurate repetitive nearshore surveys which extended out to a depth of 30 ft (9 m). Ten unique data points were used in the evaluation with measured limit depths ranging from 18 to 21 (3.9 to 6.4 m). These depths were overpredicted by an average of 4.6 ft (1.4 m). This difference could be reduced to 1.3 ft (0.4 m) by adjusting the coefficients in the equation. A reasonable correlation was also obtained using a simple multiple of wave height.

Aircraft and satellite measurement of ocean wave directional spectra using scanning-beam microwave radars

Abstract: A microwave radar technique for remotely measuring the vector wave number spectrum of the ocean surface is described. The technique which employs short-pulse, noncoherent radars in a conical scan mode near vertical incidence, is shown to be suitable for both aircraft and satellite application, the technique was validated at 10 km aircraft altitude, where we have found excellent agreement between buoy and radar-inferred absolute wave height spectra.

Wave energy saturation on a natural beach of variable slope

Abstract: Time series of flow were measured across the inner surf zone during a storm. These data were used to quantify the dependence of wave height (transformed from measured flow) and velocity on local slope and depth. Similar to previous studies, as incident waves broke and propagated into the surf zone, wave energy became saturated, and wave height was strongly dependent on depth. However, the ratio of rms wave height to local depth (γrms) was found not to be constant but to vary between 0.29 and 0.55; γrms increased with local slope and was independent of deepwater wave steepness. Thus the surf zone similarity parameter (the ratio of slope to the square root of steepness) did not adequately parameterize γrms.

The superharmonic instability of finite-amplitude water waves

Abstract: Zakharov's (1968) Hamiltonian formulation of water waves is used to prove analytically Tanaka's (1983) numerical result that superharmonic disturbances to periodic waves of permanent form exchange stability when the wave energy is an extremum as a function of wave height. Tanaka's (1985) explanation for the non-appearance of superharmonic bifurcation is also derived, and the non-existence of stability exchange when the wave speed is an extremum is explained.

Multiple longshore sand bars in the upper Chesapeake Bay

Abstract: In the upper Chesapeake Bay (Maryland, U.S.A.) field surveys were conducted at 18 multiple longshore sand bar sites. The multiple bar systems were found in water depths less than approximately 2 m (mean sea level), and exhibited mild bottom slopes of 0·0052 or less. The number of bars composing each system ranged from four to 17 and the spacing between the crests typically increased in the offshore direction, ranging from 12 to 70 m. Bar height also typically increased with distance offshore and ranged from 0·03 to 0·61 m. A grain size analysis of crest and trough sediment did not reveal any significant differences and the sediment was categorized as ‘fine sand’. A review of the literature data indicated that the Chesapeake Bay multiple bars possessed similar characteristics to those found in Gelding Bay (Baltic Sea); similarities in fetch, wave height and tidal range between the two bays may account for this finding. The surf-scaling parameter indicated that the multiple bar systems were extremely dissipative with regard to wave energy, and wave height appeared to be an important factor in controlling bar spacing and bar height. A multiple wave break point hypothesis was discussed as a possible mechanism for the formation of Chesapeake Bay multiple longshore bars, and limited observational evidence appeared to support such a mechanism.

Wave Forces on Vertical Walls

Abstract: Formulae are given for the force exerted on vertical walls: by the reflection of water waves with an arbitrary angle of incidence. The variation of the loads with all design variables show a number of unusual features, including the fact that the maximum force per unit length can be caused by obliquely-incident waves rather than standing waves. It is important for design that the whole range of possible wave conditions be considered. A method is developed for the numerical solution of the problem, which unlike the theory on which the above-mentioned formulae are based, solves the stated problem exactly. Results from the approximate formulae are compared with those from the numerical method, and are found to be surprisingly accurate over a wide range of wave conditions.

A model for Doppler peak spectral shift for low grazing angle sea scatter

Abstract: A model is formulated for Doppler spectral characteristics of radar sea scatter for low grazing angles, and is compared with previous radar measurements reported in the literature. The Doppler model is based upon the two-scale model for radar scatter, with scatterer motions hypothesized as due to the orbital wave velocity of the large-scale waves, Stokes and wind drift currents, and the phase velocity of the small-scale Bragg scatterers. Expressions for Doppler shifts due to these motions are derived, and are given as a function of wave height, wave period, and wind speed. Although this model appears to account for the peak Doppler shift of the sea-scatter Doppler spectrum for vertical polarization, it is insufficient to describe horizontally and cross-polarized data, which have larger mean Doppler shifts. However, these two cases are found to scale very closely with the nearly simultaneous vertically polarized data for the variety of environmental conditions reported. Implications of the extension of these results to higher-angle remote-sensing applications are discussed.

Significant Wave Height for Shallow Water Design

Abstract: Wave height parameters used in coastal and ocean engineering are grouped into three classes according to their definition bases: height statistics, energy, and monochromatic. Parameters within each class are easily interrelated for most engineering purposes. However, parameters from different classes are difficult to interrelate, particularly for shallow water applications where waves are near breaking. The often-used parameter “significant wave height” has traditionally been based on height statistics but many modern estimates are based on wave energy. A simple empirical method is developed to relate statistical and energy based significant height estimates. The method is developed with CERC laboratory flume data from a 1:30 plane slope, two samples of field data, and stream function wave theory. Since the two significant height estimates differ by over 40% in some laboratory cases, engineers should clearly recognize the distinction between them.

A shallow water experiment to determine the source spectrum level of wind‐generated noise

Abstract: An experiment was conducted in a shallow water region of the Mediterranean Sea to study wind‐generated noise. In addition to measuring the noise field, propagation‐loss data were collected and used in a detailed modeling of the environment. The environmental information was then used as input to a noise model based on wave theory that computes the noise field in the water column for a given (unknown) source strength. By comparing model predictions with data, the influence of the environment on recorded noise levels could be removed and a measure of the noise source spectrum levels obtained as a function of wind speed. It was found that noise levels correlate better with wind speed than with wave height. In addition it was found that the nearfield contribution dominates the noise level, with the result of producing virtually constant noise intensity over depth from moderate to high wind speeds and frequencies above 200 Hz.

Measurements of wave attenuation due to a soft bottom: The SWAMP experiment

Abstract: The Sea Wave Attenuation Measurement Program (SWAMP) was designed to provide measurements of the attenuation of waves as they travel from deep water to relatively shallow water off the Mississippi Delta. The soft bottom was suspected of causing strong attenuation in the area. This effect has now been measured. A wave staff and electromagnetic current meter were used to estimate directional wave spectra at the Cognac platform in 312 m (1025 feet) of water and at platform VV in South Pass Block 27 in 19 m (63 feet) of water. In addition, measurements of vertical bottom motion were made at platform VV. Seven storm periods from Sepember 1979 to February 1981 were studied. The directional spectral comparisons showed that the theoretically calculated refraction and shoaling can explain the changes in the spectra when the wave height is low. However, as the wave height increases, a nonlinear attenuation mechanism becomes increasingly strong. The attenuation is a strong function of deep-water wave height and a weak function of wave frequency. The bottom motion measurements showed that the bottom moved downward with small amplitude under wave crests.

Waves and longshore currents: Comparison of a numerical model with field data

Abstract: A two-dimensional numerical model is used to predict the shoaling and breaking of surface gravity waves, and the resulting longshore currents, for 5 days of the Nearshore Sediment Transport Study Santa Barbara experiment. Data with incident waves having narrow-banded frequency and directional spectra are selected for comparison in accord with the model assumptions of unidirectional and monochromatic waves. The rms wave height is used for expressing wave energy in the calculations. The current model includes bottom friction, lateral mixing, and nonliner convective accelerations. The extensive field measurements of waves, including quantitative directional information, and longshore current distributions are used to test the model results. The predicted rms wave heights are consistent with the measurements. By tuning the model with field data of longshore currents, the comparison between the model and data shows good agreement, and the obtained values of free parameters are relatively constant for the five experiment days.

Breaker Height Attenuation over Platform Coral Reefs

Abstract: This paper presents non-dimensional design charts that can be used to estimate the rate of wave height decay across platform coral reefs, the transient wave setup associated with an individual group of waves and the distance travelled before the reformation into oscillatory waves. The charts have been developed from a reanalysis of dimensional data obtained from a physical model study undertaken for a specific site and project.

Depth‐Controlled Wave Height

Abstract: A method for estimating an upperbound on the total energy of the wind wave spectrum in shallow water is extended to define a depth‐controlled zero‐moment wave height for irregular waves. The method requires an estimate of the peak frequency of the wave spectrum, knowledge of the Phillips' equilibrium coefficient, a, and water depth, h. A method for estimating α from the peak frequency of the sea spectrum and windspeed is given. Results indicate that the depth‐controlled zero‐moment wave height is generally less than the depth‐limited monochromatic wave height, Hd, and appears to vary with the square root of depth.

Stability of Armor Units on Composite Slopes

Abstract: Riprap and sandbag model tests are conducted in a wave flume to investigate the effects of berm-type slopes on the stability of armor units and wave runup as compared to uniform slopes. Measurements of wave runup, rundown, wave height, breaker type and the response of armor units under regular wave action are made for each test run. The uniform and composite slope test results are analyzed using a modified Saville’s method which accounts for the overall effects of the slope configuration on the stability of armor units and wave runup. A simple analysis procedure based on the proposed method is developed for a preliminary design of a berm configuration. An example computation is made for a composite slope protected with riprap. The berm width, the berm slope and the water depth at the shallowest point of the berm are varied so as to determine the optimal berm configuration for increasing the stability of riprap under the assumed wave conditions.

A shipborne- type wave-height meter for oceangoing vessels, using microwave Doppler radar

Abstract: A wave-height meter using a simple microwave Doppler radar, \simeq10 mW in power and 10.525 GHz in frequency, is proposed so that we can measure oceanic waves effectively while the ship is steaming. It was first applied to the measurement of the variation of water level generated in a wave tank, which suggested that it is adequately applicable to the measurement of oceanic waves. A field test was carried out off the cape of Nojimazaki by installing the Doppler radar 5 m above the sea level at the bow of the ship. The result agreed reasonably well with that measured simultaneously by the ultrasonic wave-height meter installed at the same position. Another test is running successfully on a larger ship with the wave-height meter installed at 9 m above the sea level. The significant wave height measured by the present meter is being compared with that observed visually by the navigation officers.

Wind Wave Growth in Shallow Water

Abstract: New developments in the area of shallow water wave spectra have aided in the derivation of an equation for the limiting wave height in the case of fully saturated wind seas in shallow water The result is very similar to the empirically derived expression obtained by Bretschneider in 1958 Starting with an equation for the depth controlled zero moment wave height in terms of depth, Phillip's coefficient, and the wave period associated with the peak spectral frequency, the result is obtained using a recently developed empirical experssion for the Phillip's coefficient and a method for specifying the peak spectral frequency at full development in shallow water The good comparison to Bretschneider's result is satisfying in that further validity is added to the basic equation used in the derivation and to the newer developments in shallow water spectral representations

Soil response to ocean waves

Abstract: Wave‐induced bottom pressure anomalies can result in soil motion, especially in soft deltaic deposits, that affect the design and performance of off‐shore facilities. A layered, vis‐coelastic model that includes wave‐seabottom interaction was used for a parametric study of the effects of wave degeneration, wave height, wave period, water depth, and soil properties on soil motions and the phase difference between the wave and soil motions. The effects of degradation to soil resistance due to cyclic loading are also shown with an example. The analyses were for conditions typical of the Mississippi Delta. The results presented in the paper should help the oceanographer, geotechnical engineer, and structural designer establish reasonable bounds for a preliminary design criterion and to narrow the number of analyses required to select a final design criterion.

Characteristics for extreme sea states on the norwegian continental shelf

Abstract: The characteristics for extreme sea states on the Norwegian Continental Shelf are analyzed, in terms of significant wave height and spectral peak period. Instrumental wave data from 6 different locations are used together with model data. Values for the parameters are given for return periods of 100, 10 and 1 years for each season of the year. An analytic expression for the joint probability density distribution is given. The wave spectra of extreme sea states are discussed, and the effects of climatic bias to the wave statistics are considered.

A Parametric Wind Wave Model for Arbitrary Water Depths

Abstract: A hybrid parametric wind wave model for arbitrary water depths is presented. The model is derived from an energy flux transport formulation and includes shoaling, refraction, bottom frictional dissipation, as well as finite depth modifications of the atmospheric input and nonlinear wave-wave interaction source terms. The model is applied to predict the wave characteristics resulting from a complex frontal system which passed over the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE) experimental site on October 25, 1980. The overall agreement between predicted and observed wave characteristics (significant wave height, peak frequency and mean wave direction) in 35 m water depth is considered excellent.

Redefinition of Shore-Breaker Classification as a Numerical Continuum and a Design Shore-Breaker

Abstract: Based on an initial appraisal of data, new considerations are used on which to base a least equivocal numerical definition of shore-breaking waves. Redefinition is based on the amount of the wave crest. H” b , measured from the wave crest top down, involved in shore-breaking, and is given by: H” b / H b = tanh 0.4 ξ b where H b is the shore-breaking wave height, and ξ b is a slightly modified version of the surf similarity parameter. The above equation also appears to represent the position at which the maximum impact pressure in a shore-breaking wave occurs. Relating equations are: z max / H b = 2.12 - tanh 0.4 ξ b or z max SWL / H b = 0.84 – tanh 0.4 ξ b in which z max and z max SWL the vertical distance above the bed and still water level (SWL) at shore-breaking respectively, where the maximum horizontal impact pressure occurs. Available impact pressure data indicates that the shore-breaker with the most destructive potential has a value of ξ b = 1.0. This results in a design shore-breaking wave which imparts the greatest horizontal impact at a distance of O.62 H b above the wave trough or 0.46 H b above the SWL. Recalibration of the numerical results suggests the following modification in the existing descriptive shore-breaker type scale: ξ b 5.0, surging shore-breakers.

Wave height and period at Timaru, New Zealand

Abstract: Wave data are presented for Timaru, New Zealand, based on instrumental records collected between October 1981 and October 1982. Significant wave height ranged from 0.32–3.33 m with a mean value of 0.97 m. Significant wave period ranged from 5–17 s with a mean value of 10 s. The maximum wave height recorded was 6.30 m. A marked variation was found between summer and winter conditions. Winter months displayed a much greater range of wave conditions, significant heights were generally higher and significant periods longer.

SLAR and In-Situ Observations of Wave-Current Interaction on the Columbia River Bar

Abstract: Observations at the Columbia River entrance have been com-pared to wave height amplification factors predicted by linear, one-dimensional wave-current interaction theory. A previous study found good agreement between this theory and observations, with the ex-ception of one so-called “severe event” which was seriously under-predicted. The present analysis utilizes SLAR and in-situ data to demonstrate that the probable cause of this failure is two-dimensional current refraction induced by lateral current shear. The conclusion is reached that such two-dimensional effects must be better understood if these “severe events” are to be accurately predicted on the Columbia River Bar.

Breaking of Standing Two-Components Composite and Irregular Waves

Abstract: This paper investigates, mainly from laboratory experiments, the breaking of standing two-components composite and irregular waves which are formed by a combination of the waves incident to, and reflected from, a vertical wall having a perfect reflection condition.First, the critical wave steepness of a partial standing wave in the regular wave field is proposed and its validity is confirmed by the experiments. Next, the breaking of the standing two-components composite and irregular waves is discussed. Three different kinds of breaking patterns are revealed to take place in laboratory experiments and they are classified according to the ratio of the reflected envelope wave height to the incident envelope wave height. The semi-empirical breaking limit of the standing irregular wave is proposed.